Add these lines to
/boot/config.txt and reboot Raspberry.
hdmi_force_hotplug=1
hdmi_drive=2
hdmi_force_hotplug=1 sets the Raspberry to use HDMI mode even if no HDMI monitor is detected. hdmi_drive=2 sets the Raspberry to normal HDMI mode (Sound will be sent if supported and enabled). Without this line, the Rasperry would switch to DVI (with no audio) mode by default.